Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Guan, Yongpei; Miller, Andrew J.

doi:10.1287/opre.1070.0479

Cited by 46 publications

(28 citation statements)

References 30 publications

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“…In order to deal with MIP models, modeling approaches are generally based on a set of scenarios or a scenario tree. Guan and Miller (2008) Finally, Levi and Shi (2013) develop approximation algorithms for the stochastic SILSP with random demands, lead times and dynamic forecast updates. A randomized policy is proposed with a worst-case performance guarantee of 3.…”

Section: Stochastic Modelsmentioning

confidence: 99%

Single-item dynamic lot-sizing problems: An updated survey

Brahimi

Absi

Dauzère‐Pérès

et al. 2017

European Journal of Operational Research

153

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Following our previous paper (Brahimi, N., Dauzère-Pérès, S., Najid, N. M., and Nordli, A. Single item lot sizing problems. European Journal of Operational Research, 168(1):1-16, 2006), we present an updated and extended survey of Single-Item Lot-Sizing Problems with focus on publications from 2004 to 2016. Exact and heuristic solution procedures are surveyed. A concise and comprehensive summary of different extensions of the problem is given. The classification of the extensions is based on different characteristics such as resource limitations, assumptions on demand and cost structure. The large number of surveyed papers shows the increased interest of researchers in lot-sizing problems in general and in single-item problems in particular. The survey and the proposed classification should help researchers to identify new research topics, to propose relevant problems and/or novel solution approaches.Since the publication of the seminal work of Wagner and Whitin (1958) in 1958, a lot of research has been conducted on the Single-Item Lot-Sizing Problem (SILSP) and its extensions. The SILSP is interesting in itself to model some tactical production and distribution planning problems, e.g. when planning the replenishment of one raw material with fixed and variable ordering and transportation costs. It is also important to efficiently solve the SILSP because it appears as a subproblem in the solution procedures of many complex lot-sizing problems such as capacitated multi-item problems.Extensions of the SILSP include production capacity, remanufacturing, backlogging, lost sales, demand and production time windows, bounded inventory, perishability, etc. The large number of publications on the SILSP and the large variety of its applications and extensions call for a literature review to put together all the relevant references and classify them. This will allow researchers in the field to more easily identify research trends and gaps to be filled in lot sizing in particular and in production ACCEPTED MANUSCRIPT and distribution planning in general. This survey is an extension and an update of a previous survey published by three of the authors in European Journal of Operational Research in 2006(Brahimi et al. (2006). Since this survey was published, there has been a growing interest in the study of the SILSP.There were at least 100 publications on the SILSP and its extensions in the past 8 years. The objective of this paper is to update the previous literature review and enrich it with the new research in the area. To avoid repetition and for space reasons, most of the references and details in (Brahimi et al. (2006)) are omitted.The SILSP can be defined as a planning problem in which there is time-varying demand for a single product over a planning horizon of T periods. The objective is to determine periods where production will take place and the quantities that have to be produced in these periods. The total production should satisfy the demands while minimizing the total costs. The basic costs are the unit producti...

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Section: Stochastic Modelsmentioning

confidence: 99%

Single-item dynamic lot-sizing problems: An updated survey

Brahimi

Absi

Dauzère‐Pérès

et al. 2017

European Journal of Operational Research

153

View full text Add to dashboard Cite

show abstract

“…Stochastic lot-sizing models address randomness in demands and costs. Guan and Miller (2008) study the stochastic uncapacitated lot-sizing problem with zero lead times and give a backward dynamic programming recursive algorithm which is polynomial in time with respect to the size of the scenario tree for cases when backlogging is not allowed or is prohibitively expensive. Huang and Küçükyavuz (2008) study stochastic lot-sizing problem with random lead times and give an algorithm which is polynomial with respect to the size of the scenario tree for cases with no backlogging.…”

Section: An Application: Probabilistic Lot Sizing With Service Levelsmentioning

confidence: 99%

A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints

2014

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In this paper, we consider a finite-horizon stochastic mixed-integer program involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a multi-stage (dynamic) chance-constrained program, whose deterministic equivalent is a large-scale mixedinteger program. We study the structure of the formulation, and develop a branch-and-cut method for its solution. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. We compare our dynamic model with a static chance-constrained model, a dynamic risk-averse optimization model, a robust optimization model, and a pseudo-dynamic approach, and show that significant cost savings can be achieved at high service levels using our model.

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“…Guan and Miller [23] give an algorithm for stochastic lot sizing with zero lead times that runs in polynomial time with respect to n and m. Ahmed et al [2] show that the zero inventory ordering policy, valid for the deterministic lot-sizing problem, does not hold for the stochastic case. Guan et al [22] propose a branch-and-cut algorithm to solve the stochastic lot-sizing problem with zero lead times.…”

Section: Stochastic Modelsmentioning

confidence: 99%

Mixed-Integer Optimization Approaches for Deterministic and Stochastic Inventory Management

Küçükyavuz¹

2011

2011 TutORials in Operations Research

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A fundamental problem arising in most supply chain or production operations is to determine order or production lot sizes and inventory levels to maintain high service levels and low costs. These problems are challenging both theoretically and computationally as they include concave costs representing economies-of-scale; they are dynamic; and they are subject to uncertainty in demands, costs and lead times. In addition, service level restrictions may result in chance constraints. In this tutorial, we survey recent mixed-integer optimization models and methods for various lot sizing and inventory control problems. We consider problems both when demand is dynamic and deterministic; and when demand is random following a discrete and finite nonstationary distribution over a finite planning horizon. We use polyhedral combinatorics to develop cutting planes to tighten the original mixed-integer formulations. In addition, we show how a polynomial dynamic program to solve a subproblem can be used to develop a strong extended formulation. We summarize computational experiments that illustrate the effectiveness of these methods in solving difficult capacitated multi-item order lot-sizing problems.

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Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

Cited by 46 publications

References 30 publications

Single-item dynamic lot-sizing problems: An updated survey

Single-item dynamic lot-sizing problems: An updated survey

A Branch-and-Cut Method for Dynamic Decision Making Under Joint Chance Constraints

Mixed-Integer Optimization Approaches for Deterministic and Stochastic Inventory Management

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